The Non-Strict Projection Lemma
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916159871254528 |
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| author | Meijer, T. J. Holicki, T. Eijnden, S. J. A. M. van den Scherer, C. W. Heemels, W. P. M. H. |
| author_facet | Meijer, T. J. Holicki, T. Eijnden, S. J. A. M. van den Scherer, C. W. Heemels, W. P. M. H. |
| contents | The projection lemma (often also referred to as the elimination lemma) is one of the most powerful and useful tools in the context of linear matrix inequalities for system analysis and control. In its traditional formulation, the projection lemma only applies to strict inequalities, however, in many applications we naturally encounter non-strict inequalities. As such, we present, in this note, a non-strict projection lemma that generalizes both its original strict formulation as well as an earlier non-strict version. We demonstrate several applications of our result in robust linear-matrix-inequality-based marginal stability analysis and stabilization, a matrix S-lemma, which is useful in (direct) data-driven control applications, and matrix dilation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_08735 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Non-Strict Projection Lemma Meijer, T. J. Holicki, T. Eijnden, S. J. A. M. van den Scherer, C. W. Heemels, W. P. M. H. Optimization and Control Systems and Control The projection lemma (often also referred to as the elimination lemma) is one of the most powerful and useful tools in the context of linear matrix inequalities for system analysis and control. In its traditional formulation, the projection lemma only applies to strict inequalities, however, in many applications we naturally encounter non-strict inequalities. As such, we present, in this note, a non-strict projection lemma that generalizes both its original strict formulation as well as an earlier non-strict version. We demonstrate several applications of our result in robust linear-matrix-inequality-based marginal stability analysis and stabilization, a matrix S-lemma, which is useful in (direct) data-driven control applications, and matrix dilation. |
| title | The Non-Strict Projection Lemma |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2305.08735 |